A p-adic analog of Hasse - Davenport product relation involving ∈-factors

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Abstract

In this paper we prove some generalizations of the classical Hasse-Davenport product relation for certain arithmetic factors defined on a p-adic field F, among them one finds the ∈-factors appearing in Tate's thesis. We then show that these generalizations are equivalent to some representation theoretic identities relating the determinant of ramified local coefficients matrices defined for coverings of SL2(F) to Plancherel measures and γ-factors.

Original languageEnglish
Pages (from-to)247-267
Number of pages21
JournalForum Mathematicum
Volume37
Issue number1
DOIs
StatePublished - 26 Mar 2024

Keywords

  • Hasse-Davenport product relation
  • Whittaker spaces
  • covering groups
  • epsilon factors
  • gamma factors
  • local coefficients matrices
  • local factors

All Science Journal Classification (ASJC) codes

  • General Mathematics
  • Applied Mathematics

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